"""simple docstring"""


from math import factorial, pi





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase = 30							)				->   float:




						'''simple docstring'''



						if not isinstance(__lowerCAmelCase  ,       (int, float)							):
												raise ValueError("maclaurin_sin() requires either an int or float for theta"							)

						if not isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) or accuracy <= 0:
												raise ValueError("maclaurin_sin() requires a positive int for accuracy"							)

						lowerCamelCase__   =float(__lowerCAmelCase							)
						lowerCamelCase__   =theta // (2 * pi)
						theta -= 2 * div * pi
						return sum(
						    (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1							) for r in range(__lowerCAmelCase							)							)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase = 30							)				->   float:




						'''simple docstring'''



						if not isinstance(__lowerCAmelCase  ,       (int, float)							):
												raise ValueError("maclaurin_cos() requires either an int or float for theta"							)

						if not isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) or accuracy <= 0:
												raise ValueError("maclaurin_cos() requires a positive int for accuracy"							)

						lowerCamelCase__   =float(__lowerCAmelCase							)
						lowerCamelCase__   =theta // (2 * pi)
						theta -= 2 * div * pi
						return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r							) for r in range(__lowerCAmelCase							)							)


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	print(maclaurin_sin(10))
	print(maclaurin_sin(-10))
	print(maclaurin_sin(10, 15))
	print(maclaurin_sin(-10, 15))

	print(maclaurin_cos(5))
	print(maclaurin_cos(-5))
	print(maclaurin_cos(10, 15))
	print(maclaurin_cos(-10, 15))



"""simple docstring"""


from __future__ import annotations

from typing import Any






class   __UpperCAmelCase		:

				def __init__( self      ,					_lowerCamelCase      ,					_lowerCamelCase      ,					_lowerCamelCase = 0 ):
										lowerCamelCase__   , lowerCamelCase__   =row, column
										lowerCamelCase__   =[[default_value for c in range(_lowerCamelCase )] for r in range(_lowerCamelCase )]

				def __str__( self ):
										lowerCamelCase__   =F'''Matrix consist of {self.row} rows and {self.column} columns\n'''

										# Make string identifier
										lowerCamelCase__   =0
										for row_vector in self.array:
																for obj in row_vector:
																						lowerCamelCase__   =max(_lowerCamelCase      ,					len(str(_lowerCamelCase ) ) )
										lowerCamelCase__   =F'''%{max_element_length}s'''

										# Make string and return
										def single_line(_lowerCamelCase ) -> str:
																nonlocal string_format_identifier
																lowerCamelCase__   ="["
																line += ", ".join(string_format_identifier % (obj,) for obj in row_vector )
																line += "]"
																return line

										s += "\n".join(single_line(_lowerCamelCase ) for row_vector in self.array )
										return s

				def __repr__( self ):
										return str(self )

				def 						_a      ( self      ,					_lowerCamelCase ):
										if not (isinstance(_lowerCamelCase      ,					(list, tuple) ) and len(_lowerCamelCase ) == 2):
																return False
										elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
																return False
										else:
																return True

				def __getitem__( self      ,					_lowerCamelCase ):
										assert self.validate_indicies(_lowerCamelCase )
										return self.array[loc[0]][loc[1]]

				def __setitem__( self      ,					_lowerCamelCase      ,					_lowerCamelCase ):
										assert self.validate_indicies(_lowerCamelCase )
										lowerCamelCase__   =value

				def __add__( self      ,					_lowerCamelCase ):
										assert isinstance(_lowerCamelCase      ,					_lowerCamelCase )
										assert self.row == another.row and self.column == another.column

										# Add
										lowerCamelCase__   =Matrix(self.row      ,					self.column )
										for r in range(self.row ):
																for c in range(self.column ):
																						lowerCamelCase__   =self[r, c] + another[r, c]
										return result

				def __neg__( self ):
										lowerCamelCase__   =Matrix(self.row      ,					self.column )
										for r in range(self.row ):
																for c in range(self.column ):
																						lowerCamelCase__   =-self[r, c]
										return result

				def __sub__( self      ,					_lowerCamelCase ):
										return self + (-another)

				def __mul__( self      ,					_lowerCamelCase ):

										if isinstance(_lowerCamelCase      ,					(int, float) ):  # Scalar multiplication
																lowerCamelCase__   =Matrix(self.row      ,					self.column )
																for r in range(self.row ):
																						for c in range(self.column ):
																												lowerCamelCase__   =self[r, c] * another
																return result
										elif isinstance(_lowerCamelCase      ,					_lowerCamelCase ):  # Matrix multiplication
																assert self.column == another.row
																lowerCamelCase__   =Matrix(self.row      ,					another.column )
																for r in range(self.row ):
																						for c in range(another.column ):
																												for i in range(self.column ):
																																		result[r, c] += self[r, i] * another[i, c]
																return result
										else:
																lowerCamelCase__   =F'''Unsupported type given for another ({type(_lowerCamelCase )})'''
																raise TypeError(_lowerCamelCase )

				def 						_a      ( self ):
										lowerCamelCase__   =Matrix(self.column      ,					self.row )
										for r in range(self.row ):
																for c in range(self.column ):
																						lowerCamelCase__   =self[r, c]
										return result






				def 						_a      ( self      ,					_lowerCamelCase      ,					_lowerCamelCase ):
										assert isinstance(_lowerCamelCase      ,					_lowerCamelCase ) and isinstance(_lowerCamelCase      ,					_lowerCamelCase )
										assert self.row == self.column == u.row == v.row  # u, v should be column vector
										assert u.column == v.column == 1  # u, v should be column vector

										# Calculate
										lowerCamelCase__   =v.transpose()
										lowerCamelCase__   =(v_t * self * u)[0, 0] + 1
										if numerator_factor == 0:
																return None  # It's not invertable
										return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":





	def      lowerCamelCase_					(   )				->   None:




							'''simple docstring'''



							lowerCamelCase__   =Matrix(3  ,       3  ,       0							)
							for i in range(3							):
													lowerCamelCase__   =1
							print(F'''a^(-1) is {ainv}'''							)
							# u, v
							lowerCamelCase__   =Matrix(3  ,       1  ,       0							)
							lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =1, 2, -3
							lowerCamelCase__   =Matrix(3  ,       1  ,       0							)
							lowerCamelCase__   , lowerCamelCase__   , lowerCamelCase__   =4, -2, 5
							print(F'''u is {u}'''							)
							print(F'''v is {v}'''							)
							print(F'''uv^T is {u * v.transpose()}'''							)
							# Sherman Morrison
							print(F'''(a + uv^T)^(-1) is {ainv.sherman_morrison(__lowerCAmelCase  ,       __lowerCAmelCase							)}'''							)





	def      lowerCamelCase_					(   )				->   None:




							'''simple docstring'''



							import doctest

							doctest.testmod()





	testa()


